MAE311 Lab 5 Time constants
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School
University of Alabama, Huntsville *
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Course
311L
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
Pages
6
Uploaded by KidValorSparrow43
Lab 5: Time constants
MAE 311L - Section 03
Authors:
Evan Runkle
Lab Performed Date:
10/18/2023
Due Date: 10/25/2023
Lab Instructor:
Amirreza Hesabi Shotorbani
1. Abstract
The
purpose
of
this
lab
is
to
experimentally
investigate
the
reaction
time
of
a
thermocouple and a thermometer in certain situations. The reaction time is called the
time constant of the device, and is indicated by
. The thermocouples and thermometer
τ
were moved between hot, cold, and room temperature water as shown in figure 2 to
collect temperature data and see how fast they reached equilibrium.
2. Background
Below is a list of equations used during the lab:
(1)
𝑇(𝑡) = 𝑇
∞
+ (𝑇
𝑜
− 𝑇
∞
)𝑒
−𝑡
τ
Where T(t) is temperature at time (t),
is the equilibrium temperature,
𝜏
is the time
𝑇
∞
constant in seconds that it takes the system to reach 63.2% of the difference between
the starting and equilibrium temperatures, and
is the starting temperature.
𝑇
𝑜
2
3. Data analysis and results
Table 1: Collected data from experiment
test
thermocoupl
e
T_o (C)
T_inf (C)
start time
(s)
tau time (s)
63.2% temp
(C)
time
constant (s)
1 3/16" G
5.1875
69.61585
13.75
15.80175
45.91399
2.051749
2 3/16" G
68.91827
4.664634
13.25
15.91231
28.30223
2.662314
3 3/16" G
4.517241
19.98171
15.25
17.68456
14.30367
2.430883
4 3/16" G
68.28846
20.5
17
19.29196
38.08039
2.291961
5 3/16" U
67.03125
4.042683
14.75
18.22314
27.21488
3.47314
6 3/16" U
3.454167
67.04878
15.75
21.03841
43.65363
5.288407
7 3/16" E
67.47
5.835366
13.25
15.06654
28.50948
1.81654
8 3/16" E
4.919014
65.75
18.5
19.54842
43.37153
1.048418
9 1/4" G
20.34244
43.71219
16.75
20.34244
43.71219
3.592439
10 1/8" G
3.526515
66.82927
17.25
18.64119
43.54149
1.391194
11 Thermometer
3.5
66
0
7.43
43
7.43
12 Thermometer
65
3.5
0
7.5
26.12
7.5
Figure 3: ice to boiling water temperature readings
3
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Figure 4: boiling to ice water temperature readings
Figure 5: ice to boiling water for g type thermocouples
Figure 6: boiling to ambient temperature for 3/16” G type thermocouple
4
Figure 7: Ice to ambient temperature water for 3/16” G type thermocouple
4. Questions
1.
What conclusions about time constants can be drawn from the comparative
graphs?
a.
The data from the 3/16” U thermocouples had longer time constants in ice
to boiling and boiling to ice than all but one other test indicating that they
are slower to respond then other thermocouples. The same data gathered
with the E type thermocouples has much shorter time constants and this
would mean that they are quicker to respond. 3/16” G type thermocouples
were in the middle of the two.
b.
The thermometer experiments both had longer time constants than any
other
test
by
a
significant
margin
which
is
to
be
expected
as
the
thermocouples
are
electrical
devices
and
the
thermometer
relies
on
physical properties and has to have somebody looking at it to get data so
it is much slower.
5. Conclusion
This lab was meant to show students the concept of time constant by showing the reaction time
of thermocouples and thermometers. There were some outliers but generally E type
thermocouples had the shortest time constants and this would make them reach equilibrium
faster. The thermometers had the longest time constants so they would be much slower to
reach equilibrium than the thermocouples. For many applications where you need constant
updates this is not ideal so you would want to use a thermocouple instead but if you only
occasionally need measurements and the accuracy of these measurements isn’t as important
then a thermometer would be a perfect choice.
5
6. References
6. References 1. Armentrout, D., “MAE 311L Lab 5: Time constants,” Lab Manual,
MAE Dept., Univ. Alabama in Huntsville, 2015.
6
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